Contribution to the position/force control of manipulation robots interacting with dynamic environment -- a generalization (Q1298285)

This paper studies the position and force tracking of a robotic manipulator interacting with its environment. The dynamics of the manipulator and the environment are assumed in the following form \[ \begin{cases} H(q)\ddot q+ h(q,\dot q)= u+ J^T(q)F\\ M(q)\ddot q+ L(q,\dot q)= -S^T(q)F\end{cases}\tag{\(*\)} \] where \(q\in\mathbb{R}^n\) is a vector of generalized coordinates of the manipulator/environment, \(F\in\mathbb{R}^m\), \(m<n\), denotes a force exerted by the environment to the end-effector, the matrix \(J(q)\) of size \(m\times n\) stands for the analytic Jacobian, \(u\in\mathbb{R}^n\) is a control. It is assumed that the environment generalized coordinates are a part of the manipulator coordinates. The first equation in \((*)\) refers to the manipulator dynamics, while the second one describes the dynamics of the environment. A tracking algorithm should achieve a position tracking \((q(t)\to q_d(t))\) and a force tracking \((F(t)\to F_d(t))\) with a prescribed transient response. Three tracking algorithms have been proposed that provide tracking with a desirable transient of the force (\(m\) components) and (\(n-m\)) position components \(q^1(t)\). It has been proved that the error \(q^2(t)- q^2_d(t)\) in the remaining \(m\) position components is exponentially stable.